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added gems of his own, and made from the precious raw
material a flawless work of ark -with the unmistakable impress
of his artistic individuality upon it. He delighted in perfect
things; a few of his pages will often exhibit a complete develop-
ment of one isolated result with all its implications immanent
but not loading the unique theme with expressed detail. Conse-
quently even the shortest of his papers has suggested important
developments to his successors, and his longer works are
inexhaustible mines of beautiful things.
Kronecker was what is called an 'algorist' in most of his
works. He aimed to make concise, expressive formulae tell the
story and automatically reveal the action from one step to the
next so that, when the climax was reached, it was possible to
glance back over the whole development and see the apparent
inevitability of the conclusion from the premises. Details and
accessory aids were ruthlessly pruned away until only the main
trunk of the argument stood forth in naked strength and sim-
plicity. In short, Kronecker was an artist who used mathe-
matical formulae as his medium.
After Kronecker's works on the Galois theory the subject
passed from the private ownership of a few into the common
property of all algebraists, and Kronecker had wrought so
artistically that the next phase of the theory of equations - the
current postulational formulation of the theory and its exten-
sions - can be traced back to him. His airp in algebra, like that
of Weierstrass in analysis, was to find the 'natural' way - a
matter of intuition and taste rather than scientific definition -
to the heart of his problems.
The same artistry and tendency to unification appeared in
another of his most celebrated papers, which occupied only a
couple of pages in his collected works, On the Solution of the
General Equation of the Fifth Degree, first published in 1858,
Hermite, we recall, had given the first solution, by means of
elliptic (modular) functions in the same year. Kronecker attains
Hermrte's solution - or what is practically the same - by
applying the ideas of Galois to the problem, thereby making the
miracle appear more 'natural'. In another paper, also short,
over which he has spent most of his time for five years, he